A First Course in Fuzzy Logic

A First Course in Fuzzy Logic, Fourth Edition is an expanded version of the successful third edition. It provides a comprehensive introduction to the theory and applications of fuzzy logic.This popular text offers a firm mathematical basis for the calculus of fuzzy concepts necessary for designing intelligent systems and a solid background for readers to pursue further studies and real-world applications.New in the Fourth Edition:Features new results on fuzzy sets of type-2Provides more information on copulas for modeling dependence structuresIncludes quantum probability for uncertainty modeling in social sciences, especially in economicsWith its comprehensive updates, this new edition presents all the background necessary for students, instructors and professionals to begin using fuzzy logic in its many—applications in computer science, mathematics, statistics, and engineering. About the Authors:Hung T. Nguyen is a Professor Emeritus at the Department of Mathematical Sciences, New Mexico State University. He is also an Adjunct Professor of Economics at Chiang Mai University, Thailand.Carol L. Walker is also a Professor Emeritus at the Department of Mathematical Sciences, New Mexico State University.Elbert A. Walker is a Professor Emeritus, Department of Mathematical Sciences, New Mexico State University.

The Concept of FuzzinessExamples. Mathematical modeling. Some operations on fuzzy sets. Fuzziness as uncertainty.Some Algebra of Fuzzy SetsBoolean algebras and lattices. Equivalence relations and partitions. Composing mappings. Isomorphisms and homomorphisms. Alpha-cuts. Images of alpha-level sets.Fuzzy QuantitiesFuzzy quantities. Fuzzy numbers. Fuzzy intervals. Logical Aspects of Fuzzy SetsClassical two-valued logic. A three-valued logic. Fuzzy logic. Fuzzy and Lukasiewicz logics. Interval-valued fuzzy logic.Basic Connectivest-norms. Generators of t-norms. Isomorphisms of t-norms. Negations. Nilpotent t-norms and negations. T-conforms. De Morgan systems. Groups and t-norms. Interval-valued fuzzy sets. Type-2 fuzzy sets.Additional Topics on ConnectivesFuzzy implications. Averaging operators. Powers of t-norms. Sensitivity of connectives. Copulas and t-norms.Fuzzy RelationsDefinitions and examples. Binary fuzzy relations. Operations on fuzzy relations. Fuzzy partitions. Fuzzy relations as Chu spaces. Approximate reasoning. Approximate reasoning in expert systems. A simple form of generalized modus ponens. The compositional rule of inference.Universal Approximation Fuzzy rule bases. Design methodologies. Some mathematical background. Approximation capability. Possibility TheoryProbability and uncertainty. Random sets. Possibility measures. Partial KnowledgeMotivations. Belief functions and incidence algebras. Monotonicity. Beliefs, densities, and allocations. Belief functions on infinite sets. Mobius transforms of set-functions. Reasoning with belief functions. Decision making using belief functions. Rough sets. Conditional events.Fuzzy MeasuresMotivation and definitions. Fuzzy measures and lower probabilities. Fuzzy measures in other areas. Conditional fuzzy measures.The Choquet IntegralThe Lebesgue integral. The Sugeno integral. The Choquet integral. Fuzzy Modeling and ControlMotivation for fuzzy control. The methodology of fuzzy control. Optimal fuzzy control. An analysis of fuzzy control techniques.

Hung T. Nguyen is a Professor Emeritus at the Department of Mathematical Sciences, New Mexico State University. He is also an Adjunct Professor of Economics at Chiang Mai University, Thailand.Carol L. Walker is also a Professor Emeritus at the Department of Mathematical Sciences, New Mexico State University.Elbert A. Walker is a Professor Emeritus, Department of Mathematical Sciences, New Mexico State University.